How do I UV Unwrap Part of my Object?
This works in Blender 2.74



Select your mesh, enter edit mode, and select only the faces that you want to unwrap. Now press U and select the type of unwrap you want to use:



Notice that when I select other faces, the only visible selection is a vertice on the lower left, while an unwrapped face becomes fully visible when selected in the viewport. Basically, Blender automatically unwraps the selected part of the mesh, and then sends all other vertices to 0, 0 as there is no coordinate information to display for them. However they do still display a color:





What you can do is to assign a different material to the not unwrapped vertices so that you can control the color easily. Select all the unwrapped faces and press Ctrl+I to invert the selection. Now go to the materials panel and make a new material, and press the Assign button: